We are asked to find the
surface area of a
regular hexagonal prism, and round it to the nearest square inch.
---
🔷 Step 1: Understand the Shape
A
regular hexagonal prism has:
- Two congruent regular hexagon bases (top and bottom)
- Six rectangular lateral faces
The surface area is:
$$
\text{Surface Area} = 2 \times (\text{Area of base}) + (\text{Perimeter of base}) \times (\text{Height of prism})
$$
---
🔷 Given Dimensions
From the image:
- The
height of the prism (length of the side face) is
8 inches
- The
side length of the hexagon is
2 inches
- The
apothem (distance from center to midpoint of a side) is
1.7 inches
> Note: In a regular hexagon, the apothem is the perpendicular distance from the center to a side.
---
🔷 Step 2: Area of One Hexagonal Base
For a regular polygon, the area is:
$$
\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}
$$
For a regular hexagon with side length $ s = 2 $ in:
- Perimeter $ P = 6 \times 2 = 12 $ in
- Apothem $ a = 1.7 $ in
So,
$$
\text{Area of one base} = \frac{1}{2} \times 12 \times 1.7 = 6 \times 1.7 = 10.2 \text{ in}^2
$$
Then, two bases:
$$
2 \times 10.2 = 20.4 \text{ in}^2
$$
---
🔷 Step 3: Lateral Surface Area
Each of the 6 rectangular sides has:
- Width = side of hexagon = 2 in
- Height = 8 in
So, area of one rectangle = $ 2 \times 8 = 16 $ in²
Total lateral area = $ 6 \times 16 = 96 $ in²
Alternatively, using formula:
$$
\text{Lateral Area} = \text{Perimeter of base} \times \text{Height of prism} = 12 \times 8 = 96 \text{ in}^2
$$
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🔷 Step 4: Total Surface Area
$$
\text{Total SA} = \text{Base Areas} + \text{Lateral Area} = 20.4 + 96 = 116.4 \text{ in}^2
$$
---
🔷 Final Answer
Round to the nearest square inch:
$$
\boxed{116} \text{ in}^2
$$
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✔ Answer: 116 square inches
Parent Tip: Review the logic above to help your child master the concept of hexagonal prism surface area worksheet.
